4-13k=-5k^2-4k

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Solution for 4-13k=-5k^2-4k equation:


Simplifying
4 + -13k = -5k2 + -4k

Reorder the terms:
4 + -13k = -4k + -5k2

Solving
4 + -13k = -4k + -5k2

Solving for variable 'k'.

Combine like terms: -13k + 4k = -9k
4 + -9k + 5k2 = -4k + -5k2 + 4k + 5k2

Reorder the terms:
4 + -9k + 5k2 = -4k + 4k + -5k2 + 5k2

Combine like terms: -4k + 4k = 0
4 + -9k + 5k2 = 0 + -5k2 + 5k2
4 + -9k + 5k2 = -5k2 + 5k2

Combine like terms: -5k2 + 5k2 = 0
4 + -9k + 5k2 = 0

Factor a trinomial.
(4 + -5k)(1 + -1k) = 0

Subproblem 1

Set the factor '(4 + -5k)' equal to zero and attempt to solve: Simplifying 4 + -5k = 0 Solving 4 + -5k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5k = 0 + -4 -5k = 0 + -4 Combine like terms: 0 + -4 = -4 -5k = -4 Divide each side by '-5'. k = 0.8 Simplifying k = 0.8

Subproblem 2

Set the factor '(1 + -1k)' equal to zero and attempt to solve: Simplifying 1 + -1k = 0 Solving 1 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1k = 0 + -1 -1k = 0 + -1 Combine like terms: 0 + -1 = -1 -1k = -1 Divide each side by '-1'. k = 1 Simplifying k = 1

Solution

k = {0.8, 1}

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